Snapback Repellers in Chaos Theory and their Application in Ecology
碩士 === 國立交通大學 === 應用數學系所 === 98 === This work briefly reviews the history of chaos theory and elucidates the relationship among chaos, Lyapunov exponent, topological entropy, strange attractor, snapback repeller, and Sarkovskii's theorem, connecting them to each other using a relational graph....
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ndltd-TW-098NCTU55070132016-04-18T04:21:30Z http://ndltd.ncl.edu.tw/handle/12384229665052138639 Snapback Repellers in Chaos Theory and their Application in Ecology 混沌理論之速返斥子在生態學上的應用 Chen, Hsun-Hui 陳勛暉 碩士 國立交通大學 應用數學系所 98 This work briefly reviews the history of chaos theory and elucidates the relationship among chaos, Lyapunov exponent, topological entropy, strange attractor, snapback repeller, and Sarkovskii's theorem, connecting them to each other using a relational graph. Mathematical and computer-assisted tools can be used to determine whether maps or systems are chaotic by finding a quantity or sometimes identifying the existence of a property. In ecology, Satake's generalized resource budget model that modified from Isagi's resource budget model, Satake and Iwasa proved by computing the positive Lyapunov exponent that if the depletion coefficient k is greater than one, then the system is chaotic. However, a positive Lyapunov exponent means only sensitivity in Devaney's chaos. Therefore, this work presents mathematical views and a numerical analysis on Satake's model, using the "snapback repeller method" to prove that the model is chaotic in Devaney's sens (involving transitivity, density, and sensitivity). Moreover, this work also overcomes the omission of Satake's paper (Satake & Iwasa, 2000) when the depletion coefficient k is a positive integer. Furthermore, the end of this work investigates the difference between odd depletion coefficients and even depletion coefficients. Chang, Shu-Ming 張書銘 2010 學位論文 ; thesis 47 zh-TW |
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碩士 === 國立交通大學 === 應用數學系所 === 98 === This work briefly reviews the history of chaos theory and elucidates the relationship among chaos, Lyapunov exponent, topological entropy, strange attractor, snapback repeller, and Sarkovskii's theorem, connecting them to each other using a relational graph. Mathematical and computer-assisted tools can be used to determine whether maps or systems are chaotic by finding a quantity or sometimes identifying the existence of a property. In ecology, Satake's generalized resource budget model that modified from Isagi's resource budget model, Satake and Iwasa proved by computing the positive Lyapunov exponent that if the depletion coefficient k is greater than one, then the system is chaotic. However, a positive Lyapunov exponent means only sensitivity in Devaney's chaos. Therefore, this work presents mathematical views and a numerical analysis on Satake's model, using the "snapback repeller method" to prove that the model is chaotic in Devaney's sens (involving transitivity, density, and sensitivity). Moreover, this work also overcomes the omission of Satake's paper (Satake & Iwasa, 2000) when the depletion coefficient k is a positive integer. Furthermore, the end of this work investigates the difference between odd depletion coefficients and even depletion coefficients.
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author2 |
Chang, Shu-Ming |
author_facet |
Chang, Shu-Ming Chen, Hsun-Hui 陳勛暉 |
author |
Chen, Hsun-Hui 陳勛暉 |
spellingShingle |
Chen, Hsun-Hui 陳勛暉 Snapback Repellers in Chaos Theory and their Application in Ecology |
author_sort |
Chen, Hsun-Hui |
title |
Snapback Repellers in Chaos Theory and their Application in Ecology |
title_short |
Snapback Repellers in Chaos Theory and their Application in Ecology |
title_full |
Snapback Repellers in Chaos Theory and their Application in Ecology |
title_fullStr |
Snapback Repellers in Chaos Theory and their Application in Ecology |
title_full_unstemmed |
Snapback Repellers in Chaos Theory and their Application in Ecology |
title_sort |
snapback repellers in chaos theory and their application in ecology |
publishDate |
2010 |
url |
http://ndltd.ncl.edu.tw/handle/12384229665052138639 |
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